y(7) −4y(6) −4y(5) + 56y(4) −156y(3) + 224y'' −176y' + 64y = ex cos(x)−3e2x + xe−4x Which is the special equation form of the equation ? a) y = (A1x2 + A2x)e−4x + A3e2x + A4xex cos(x) + A5xex sin(x) b) y= A1xe2x + (A2x + A3)e4x + A4ex cos(x) + A5ex cos(x) c) y = A1xex cos(x) + A2xex sin(x) + A3x2e2x + (A4x + A5)e−4x d) y = A1x2ex cos(x) + A2x2ex sin(x) + A3x2e2x + (A4x2 + A5x)e−4x e) y= A1x2e2x + (A2x + A3)e−4x + A4ex cos(x) + A5ex sin(x) f) y= A1e2x + A2xex cos(x) + A3xex sin(x) + (A4x + A5)e−4
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
y(7) −4y(6) −4y(5) + 56y(4) −156y(3) + 224y'' −176y' + 64y = ex cos(x)−3e2x + xe−4x
Which is the special equation form of the equation ?
a) y = (A1x2 + A2x)e−4x + A3e2x + A4xex cos(x) + A5xex sin(x)
b) y= A1xe2x + (A2x + A3)e4x + A4ex cos(x) + A5ex cos(x)
c) y = A1xex cos(x) + A2xex sin(x) + A3x2e2x + (A4x + A5)e−4x
d) y = A1x2ex cos(x) + A2x2ex sin(x) + A3x2e2x + (A4x2 + A5x)e−4x
e) y= A1x2e2x + (A2x + A3)e−4x + A4ex cos(x) + A5ex sin(x)
f) y= A1e2x + A2xex cos(x) + A3xex sin(x) + (A4x + A5)e−4x
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